Dielectric Dilemma

Abstract

A dielectric dilemma faces scientists because Maxwell's equations are poor approximations as usually written, with a single dielectric constant. Maxwell's equations are then not accurate enough to be useful in many applications involving ionic solutions and even solids. The dilemma can be partially resolved by a rederivation of conservation of current, where current is defined now to include the 'polarization of the vacuum' $\epsilon_0 \frac{\partial E}{\partial t}$. Conserveration of current becomes Kirchoff's current law with this definition, in the one dimensional circuits of our electronic technology. With this definition, Kirchoff's laws are valid whenever Maxwell's equations are valid, explaining why those laws are able to describe circuits that switch in nanoseconds.